Propagation of Rayleigh Waves in a Rotating Fiber-Reinforced Medium under the Action of Uniform Magnetic Field and Gravity
Maity N, Barik SP and Chaudhuri PK
Published on: 2021-01-25
This paper is concerned with the study of Rayleigh waves in a rotating fiber-reinforced electrically conducting elastic solid medium under magnetic field and gravity. The magnetic field is applied in such a direction that the problem can be considered as a two dimensional one. The combined effect of magnetic field, electrical conductivity, rotation, gravity and the reinforcement of the medium on the propagation of Rayleigh waves have been studied. The effects on various subjects of interest are discussed and shown graphically.
KeywordsRayleigh waves; Fiber-reinforced medium; Magnetic permeability and Electric conductivity; Rotational effect; Gravity field; Wave velocity
The concept of fiber-reinforced solids stems from the necessity of generating more strength, stiffness and load bearing capacity of solids through the process of suitably mixing certain kind of materials with such solids. In situations where light material with high strength and stiffness is essential, as for example, in manufacturing aircraft components, fiber-reinforced material can be a good option. Fiber-reinforcing is not any new idea. In fact, fiber-reinforcing in its crude form was a common practice followed in hardening soil by mixing straw dust or rice husk with the soil in early stages of civilization and is still followed in some rural areas. Another very common instance is the use of iron wire/rods in manufacturing concrete structures. With the advancement of technology and innovation of modern methods, different kinds of materials are manufactured as per need using fiber-reinforcing concept. Different methods are adopted in fiber-reinforcing process, viz., long fibers are arranged in parallel in the matrix, short fibers are randomly arranged in the matrix, or fibers in the form of cloth are set in the matrix. Obviously, the strength and the load bearing capacity of the fiber-reinforced material will depend upon the fiber arrangement in the matrix. Arunakanthi and Kumar  has an experimental studies on fiber-reinforced Concrete.
It is known that the surface waves play a crucial role in the study of earthquakes, geophysics and geodynamics. Well-known general surface waves are Rayleigh waves, Love waves and Stoneley waves. They are well connected with earthquake spectrum analysis. Rayleigh waves are responsible for causing destruction to the structure owing to its slower attenuation of the energy than that of the body waves. In classical theory of elasticity, gravity effect is generally neglected. The effect of gravity on wave propagation in an elastic solid medium was first considered by Bromwich . He has treated the force of gravity as a type of body force. Love  extended the work of Bromwich and investigated the influence of gravity on superficial waves and showed that the Rayleigh wave velocity is affected by the gravity field. Biot  studied the influence of gravity on Rayleigh waves, assuming the force of gravity to create a type of initial stress of hydrostatic nature and the medium as incompressible. De and Sengupta [5-7] studied the effect of gravity on the propagation of surface waves in an elastic layer and also on Lamb's problem on a plane. Das et al  investigated surface waves under the influence of gravity in a non-homogeneous elastic solid medium. Abd-Alla et al.  studied the surface waves propagation in a fiber-reinforced anisotropic elastic media subjected to gravity field. Abd-Alla et al.  also investigated the Propagation of Rayleigh waves in magneto-thermo-elastic half-space of a homogeneous orthotropic material under the effect of rotation. Abo-Dahab et al.  studied the effect of gravity field, initial stress and rotation on the S-waves propagation in a non-homogeneous anisotropic medium under magnetic field. Bayones [12,13] investigated propagation of Rayleigh waves in fiber-reinforced anisotropic thermo-visco elastic media under the effect of rotation. Abd-Alla et al.  investigated the effects of rotation and gravity field on surface waves in fiber-reinforced thermoelastic media under four theories. Maity et al. [15,16] investigated the wave propagation in a rotating fiber-reinforced poro-elastic solid under the action of uniform magnetic field and also propagation of plane waves in a rotating magneto thermoelastic fiber-reinforced medium with voids under G-N theory. Sethi et.al.  Studied surface waves in fiber-reinforced anisotropic elastic media under the influence of gravity. Abd-Alla et al.  discussed the effect of rotation, magnetic field, initial stress and gravity on Rayleigh waves in a homogeneous orthotropic elastic half-space.